If A(1, 3) and B(2, 1) are points, find the equation of the locus of p

1.	If A(1, 3) and B(2, 1) are points, find the equation of the locus of point P such that PA = PB.
Answer» Let P(x, y) be any point on the required locus. Given, A(1, 3), B(2, 1) and PA = PB ∴ PA² = PB² ∴ (x – 1)² + ( y – 3)² = (x – 2)² + (y – 1)² ∴ x² – 2x + 1 + y² – 6y + 9 = x² – 4x + 4 + y² – 2y + 1 -2x – 6y + 10 = -4x – 2y + 5 ∴ 2x – 4y + 5 = 0 ∴ The required equation of locus is 2x – 4y + 5 = 0.

If A(1, 3) and B(2, 1) are points, find the equation of the locus of point P such that PA = PB.

Answer»

Let P(x, y) be any point on the required locus. Given, A(1, 3), B(2, 1) and PA = PB

∴ PA² = PB²

∴ (x – 1)² + ( y – 3)² = (x – 2)² + (y – 1)²

∴ x² – 2x + 1 + y² – 6y + 9 = x² – 4x + 4 + y² – 2y + 1 -2x – 6y + 10 = -4x – 2y + 5

∴ 2x – 4y + 5 = 0

∴ The required equation of locus is 2x – 4y + 5 = 0.